BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Dalimil Mazac (IAS) DTSTART:20201214T150000Z DTEND:20201214T160000Z DTSTAMP:20260422T212556Z UID:SpherePackingAndCFT/1 DESCRIPTION:Title: An introduction to the conformal bootstrap for mathematicians< /a>\nby Dalimil Mazac (IAS) as part of Sphere packing and the conformal bo otstrap\n\n\nAbstract\nConformal field theories are a rich class of quantu m field theories that can be defined and studied fully rigorously in a gen eral number of dimensions. In fact\, the definition of a conformal field t heory in n dimensions fits in one line: It is a unitary representation V o f the conformal group G=the universal cover of SO(2\,n)\, which is a direc t sum of irreducible lowest-weight modules\, and which admits a certain ki nd of G-invariant multiplication. In my talk\, I will explain this definit ion and some of its consequences. In particular\, I will review that the d efinition implies stringent bounds on the weights of the irreducible compo nents in V. These bounds are typically obtained using linear and/or semi-d efinite programming. The bounds are often sharp -- saturated by physical c onformal field theories. In certain special cases\, the sharpness of the b ounds can be proved using magic functions for sphere packing in 8 and 24 d imensions. The ultimate goal of the conformal bootstrap is to classify con formal field theories starting from the above definition. The most tantali zing finding is that the bounds reveal the existence of many non-trivial s olutions of the axioms\, yet no explicit description of any non-trivial so lution is presently known in n>2.\n LOCATION:https://researchseminars.org/talk/SpherePackingAndCFT/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Amir Tajdini (UCSB) DTSTART:20201214T180000Z DTEND:20201214T190000Z DTSTAMP:20260422T212556Z UID:SpherePackingAndCFT/2 DESCRIPTION:Title: Fast conformal bootstrap and high-dimensional sphere packing\nby Amir Tajdini (UCSB) as part of Sphere packing and the conformal boo tstrap\n\n\nAbstract\nThe conformal bootstrap program seeks to map the spa ce of possible conformal field theories and to identify those on the bound ary of theory space. In this talk\, I will discuss a numerical method that is applicable to certain bootstrap problems\, such as the spin-less modul ar bootstrap in two dimensions. This method extends the conformal bootstra p to the regime of a large number of degrees of freedom which is relevant to the physics of black holes in three-dimensional gravity. The same metho d applies to the sphere packing problem and gives new bounds on the packin g density in high dimensions. I will talk about these new bounds and give a summary of existing bounds for these problems.\n LOCATION:https://researchseminars.org/talk/SpherePackingAndCFT/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Henry Cohn (Microsoft Research) DTSTART:20201215T150000Z DTEND:20201215T160000Z DTSTAMP:20260422T212556Z UID:SpherePackingAndCFT/3 DESCRIPTION:Title: An introduction to sphere packing\nby Henry Cohn (Microsof t Research) as part of Sphere packing and the conformal bootstrap\n\nAbstr act: TBA\n LOCATION:https://researchseminars.org/talk/SpherePackingAndCFT/3/ END:VEVENT BEGIN:VEVENT SUMMARY:David Simmons-Duffin (Caltech) DTSTART:20201215T180000Z DTEND:20201215T190000Z DTSTAMP:20260422T212556Z UID:SpherePackingAndCFT/4 DESCRIPTION:Title: Introduction to the crossing equation in higher dimensional CF Ts\nby David Simmons-Duffin (Caltech) as part of Sphere packing and th e conformal bootstrap\n\n\nAbstract\nIn a continuation of Dalimil's talk o n Monday\, I will\ndiscuss the crossing equation for higher dimensional CF Ts and explain\nsome analytical results that have been derived from it.\n LOCATION:https://researchseminars.org/talk/SpherePackingAndCFT/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Fernando Oliveira (TU Delft) DTSTART:20201216T150000Z DTEND:20201216T160000Z DTSTAMP:20260422T212556Z UID:SpherePackingAndCFT/5 DESCRIPTION:Title: A quick introduction to conic programming\nby Fernando Oli veira (TU Delft) as part of Sphere packing and the conformal bootstrap\n\n \nAbstract\nConic programming is a general optimization framework that enc ompasses both linear and semidefinite programming. I will give a brief ove rview of the theory of conic programming\, with an eye towards application s to problems like the kissing number problem or the sphere packing proble m.\n LOCATION:https://researchseminars.org/talk/SpherePackingAndCFT/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Alex Maloney (McGill University) DTSTART:20201216T180000Z DTEND:20201216T190000Z DTSTAMP:20260422T212556Z UID:SpherePackingAndCFT/6 DESCRIPTION:Title: The Siegel-Weil formula and quantum gravity as an average\ nby Alex Maloney (McGill University) as part of Sphere packing and the con formal bootstrap\n\n\nAbstract\nI will explore the idea that certain theor ies of gravity are not traditional quantum theories\, but are instead aver ages over ensembles of quantum theories. I will consider the average over free boson conformal field theories in two dimensions\, and compute the ge nus g partition function using the Siegel-Weil formula. The result is a re al analytic Eisenstein series which can be interpreted as the sum over geo metries in a certain exotic - but in a sense exactly solvable - theory of quantum gravity. The techniques used are similar to those used to study hi gh dimensional sphere packing by averaging over spaces of lattices\, sugge sting an analogy between semi-classical gravity and a theory of random lat tices (or sphere packings) in high dimensions.\n LOCATION:https://researchseminars.org/talk/SpherePackingAndCFT/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Sylvia Serfaty (NYU) DTSTART:20201217T150000Z DTEND:20201217T160000Z DTSTAMP:20260422T212556Z UID:SpherePackingAndCFT/7 DESCRIPTION:Title: Microscopic description of Coulomb gases\nby Sylvia Serfat y (NYU) as part of Sphere packing and the conformal bootstrap\n\n\nAbstrac t\nI will review some results on the arrangements of systems of points wit h Coulomb\, logarithmic or more generally Riesz interactions (i.e. inverse powers of the distance)\, possibly with temperature. Motivations come fro m quantum physics\, statistical mechanics\, random matrix theory\, approxi mation theory... We will take a point of view based on the detailed expans ion of the interaction energy to describe the microscopic patterns formed by the points and local laws on the discrepancies. This allows to observe the effect of the temperature as it gets very large or very small\, and to connect with crystallization questions.\n LOCATION:https://researchseminars.org/talk/SpherePackingAndCFT/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Maryna Viazovska (EPFL) DTSTART:20201217T180000Z DTEND:20201217T190000Z DTSTAMP:20260422T212556Z UID:SpherePackingAndCFT/8 DESCRIPTION:Title: Colloquium: Sphere packings\, universal optimality\, and Fouri er interpolation\nby Maryna Viazovska (EPFL) as part of Sphere packing and the conformal bootstrap\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/SpherePackingAndCFT/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Sridip Pal (IAS) DTSTART:20201218T150000Z DTEND:20201218T160000Z DTSTAMP:20260422T212556Z UID:SpherePackingAndCFT/9 DESCRIPTION:Title: Modular bootstrap at high energy and Beurling-Selberg extremiz ation\nby Sridip Pal (IAS) as part of Sphere packing and the conformal bootstrap\n\n\nAbstract\nWe consider the universality of existence and sa turation of asymptotic bounds in various quantities in 2D conformal field theory (CFT) . In particular\, we obtain the lower and upper bounds on the number of operators within a high energy interval [Δ−δ\,Δ+δ]\, of a modular invariant 2D CFT with a positive spectral density. These bounds depend on a choice of functions that majorize and minorize the characteris tic function of the interval [Δ−δ\,Δ+δ] and have Fourier transforms of finite support. The optimization of the bounds over this choice turns o ut to be exactly the Beurling-Selberg extremization problem\, widely known in analytic number theory. We review solutions of this problem and presen t the corresponding bounds on the number of operators. When 2δ ∈ Z≥0 the bounds are saturated by known partition functions with integer-spaced spectra. Similar results apply to operators of fixed spin and Virasoro pri maries in c > 1 theories. If time permits\, I will briefly sketch over how the analysis can be generalized for asymptotics of OPE coefficient\, poss ibly with some additional numerical input and for CFTs with global symmetr y.\n LOCATION:https://researchseminars.org/talk/SpherePackingAndCFT/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Felipe Gonçalves (University of Bonn) DTSTART:20201218T180000Z DTEND:20201218T190000Z DTSTAMP:20260422T212556Z UID:SpherePackingAndCFT/10 DESCRIPTION:Title: Sign uncertainty\nby Felipe Gonçalves (University of Bon n) as part of Sphere packing and the conformal bootstrap\n\n\nAbstract\nl will talk about the recent developments of the sign uncertainty principle and its relation with sphere packing. Time permitting we will explore some of the new results in [New Sign Uncertainty Principles\, arxiv.org/abs/20 03.10771].\n LOCATION:https://researchseminars.org/talk/SpherePackingAndCFT/10/ END:VEVENT END:VCALENDAR